The Occupational Safety and Health Administration (OSHA) requires employers to implement a hearing conservation program when noise exposure is at or above 85 decibels averaged over 8 working hours. A hospital wanted to examine their noise levels and so measured the noise levels in 84 corridors. They found the mean noise level was 61.2 decibels and the standard deviation was 7.9 decibels. (You may use R or the appendices from the book to support finding the probabilities.) a) Find the 99% confidence interval of the true mean noise level? b) Would you expect the 95% confidence interval to be wider or narrower than the 99% confidence interval found in part (a)? Draw a sketch of the regions to support justifying your answer. What does the confidence interval for a mean represent? c) Find the 99% confidence interval on the noise level variance. d) Find the 99% confidence interval of the true mean noise level if the same mean and standard deviation were observed, but only 4 corridors were sampled. e) Is the answer to part (c) wider, narrower, or equal to part (a)? Why is this response the case? Justify your